SVbound {SelectionBias}

Smith and VanderWeele bound

Description

SVbound() returns a list with the SV bound. All sensitivity parameters for the population of interest must be set to numbers, and the rest can be left as NULL. The sensitivity parameters can be inserted directly or as output from sensitivityparametersM(). If the causal estimand is expected to be larger than the observational estimand, the recoding of the treatment has to be done manually.

Usage

SVbound(
  whichEst,
  pY1_T1_S1,
  pY1_T0_S1,
  RR_UY_T1 = NULL,
  RR_UY_T0 = NULL,
  RR_SU_T1 = NULL,
  RR_SU_T0 = NULL,
  RR_UY_S1 = NULL,
  RR_TU_S1 = NULL
)

Arguments

whichEst

Input string. Defining the causal estimand of interest. Available options are as follows. (1) Relative risk in the total population: "RR_tot", (2) Risk difference in the total population: "RD_tot", (3) Relative risk in the subpopulation: "RR_sub", (4) Risk difference in the subpopulation: "RD_sub".

pY1_T1_S1

Input value. The probability P(Y=1|T=1,I_S=1). Must be between 0 and 1.

pY1_T0_S1

Input value. The probability P(Y=1|T=0,I_S=1). Must be between 0 and 1.

RR_UY_T1

Input value. The sensitivity parameter RR_UY|T=1. Must be greater than or equal to 1. Used in the bounds for the total population.

RR_UY_T0

Input value. The sensitivity parameter RR_UY|T=0. Must be greater than or equal to 1. Used in the bounds for the total population.

RR_SU_T1

Input value. The sensitivity parameter RR_SU|T=1. Must be greater than or equal to 1. Used in the bounds for the total population.

RR_SU_T0

Input value. The sensitivity parameter RR_SU|T=0. Must be greater than or equal to 1. Used in the bounds for the total population.

RR_UY_S1

Input value. The sensitivity parameter RR_UY|S=1. Must be greater than or equal to 1. Used in the bounds for the subpopulation.

RR_TU_S1

Input value. The sensitivity parameter RR_TU|S=1. Must be greater than or equal to 1. Used in the bounds for the subpopulation.

Value

A list containing the Smith and VanderWeele bound.

References

Smith, Louisa H., and Tyler J. VanderWeele. "Bounding bias due to selection." Epidemiology (Cambridge, Mass.) 30.4 (2019): 509.

Zetterstrom, Stina and Waernbaum, Ingeborg. "Selection bias and multiple inclusion criteria in observational studies" Epidemiologic Methods 11, no. 1 (2022): 20220108.

Examples

# Example for relative risk in the total population.
SVbound(whichEst = "RR_tot", pY1_T1_S1 = 0.05, pY1_T0_S1 = 0.01,
 RR_UY_T1 = 2, RR_UY_T0 = 2, RR_SU_T1 = 1.7, RR_SU_T0 = 1.5)

# Example for risk difference in the total population.
SVbound(whichEst = "RD_tot", pY1_T1_S1 = 0.05, pY1_T0_S1 = 0.01,
 RR_UY_T1 = 2, RR_UY_T0 = 2, RR_SU_T1 = 1.7, RR_SU_T0 = 1.5)

# Example for relative risk in the subpopulation.
SVbound(whichEst = "RR_sub", pY1_T1_S1 = 0.05, pY1_T0_S1 = 0.01,
 RR_UY_S1 = 2.71, RR_TU_S1 = 2.33)

# Example for risk difference in the subpopulation.
SVbound(whichEst = "RD_sub", pY1_T1_S1 = 0.05, pY1_T0_S1 = 0.01,
 RR_UY_S1 = 2.71, RR_TU_S1 = 2.33)